Question

Find the largest number of 3 digits which is a perfect square?​

Answer 1

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We know, the largest three-digit number is 999.

Also, our knowledge of elementary mathematics reminds us that:

(a + b)^2 = a^2 + 2 * a * b + b^2.

We know, 30^2 = 900; which is not very far from 999.

Putting a = 30 in the above equation, we get:

(30 + b)^2 = 30^2 + 2 * 30 * b + b^2

Or, (30 + b)^2 = 900 + 60b + b^2

Now, we have to check out for what largest integer value of b, the value of (60b + b^2) remains less than or equal to 99.

Clearly b = 2 takes 60b to 120; so we can't take it.

For b = 1; (60b + b^2) = 61 and this meets our requirement.

So, the largest three-digit number which is a perfect square is (30 + 1)^2 = 31^2 = 961

Answer 2

Answer:

So if 38 will be addede to 999 then it will become a 4 digit number. Therefore to find the largest 3 digit perfect square we will subtract 38 from 999. 999 - 38 = 961. Hence 961 isthe largest 3 digit perfect square whose square root is 31.